Thanks for the replies, as it turns out it was nothing to do with /etc/exports or regular file system permissions.
Synology have applied their own brand of Access Control Lists (ACLs) to shared folders.
Basically I had to run the following commands to allow vdsm:kvm (36:36) to read and write to the share:
EXPORT_DIR=/volumeX/...
synoacltool -set-owner "$EXPORT_DIR" group kvm:allow:rwxpdDaARWcCo:fd--
synoacltool -add "$EXPORT_DIR" user:vdsm:allow:rwxpdDaARWcCo:fd--
synoacltool -add "$EXPORT_DIR" group:kvm:allow:rwxpdDaARWcCo:fd--